CANTON - Count on Cantor

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One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.

1/1 1/2 1/3 1/4 1/5 ...
2/1 2/2 2/3 2/4
3/1 3/2 3/3
4/1 4/2
5/1

In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.

Input

The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.

Then, it contains a single number per line.

Output

You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.

Example

Input:
3
3
14
7

Output:
TERM 3 IS 2/1
TERM 14 IS 2/4
TERM 7 IS 1/4

hide comments
yead_025: 2017-11-15 15:04:53

O(1)

sanyam19: 2017-10-23 21:18:02

AC in one go.....one should first observe d pattern..if want to make a formula,try to observe num nd den...

Last edit: 2017-10-23 21:18:32
sohailwiiierd: 2017-10-21 21:00:44

the corners..........

hitesh87: 2017-09-27 20:22:20

Very nice problem. AC in one go.

bhuvi9: 2017-08-17 11:51:59

took 5 hours to solve it.

imranjeetsingh: 2017-07-12 16:08:17

took some time but AC in one go.

Last edit: 2017-07-12 16:14:29
manish_nit97: 2017-07-03 21:16:37

After thinking for the pattern at a continuous stretch of 1.5 hours finally got the logic.
Nothing to do with programming here ....no recursion, no algo......it's pure number game and algebra!
AC in 1 GO!!.....The hard work paid off..
it's really worth doing.....cheers

dr_br34k: 2017-06-27 14:58:37

Think of O(1) solution every ith new slant line is made of i elements.

anilkumar1998: 2017-06-09 19:44:47

Try to think of O(1) solution.

codervrinda: 2017-05-29 07:09:27

nice problem:) !


Added by:Thanh-Vy Hua
Date:2005-02-27
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET
Resource: ACM South Eastern European Region 2004